Study on the emergency capacity of coal mine enterprises in Longdong Area based on D-FAHP method

Emergency capability assessment is a complex system with multiple factors, variables and levels. Incomplete and uncertain assess information often occurs during assessment. Based on this, a method combining D-number theory and fuzzy analytic Hierarchy process (FAHP) is proposed to study the emergency capacity of coal enterprises in Longdong area. On the basis of analyzing the limitation of D-S evidence theory, the D-number theory was optimized and improved. According to the principles of systematicness, feasibility, scientificity and timeliness, a hierarchical structure model of enterprise emergency capability assessment was constructed from the perspective of pre-incident, mid-incident and post-incident, which consisted of 4 first-level indicators and 18 s-level indicators. The weight and importance of the assessment index of emergency response capability are calculated by organically integrating the D-number preference relation with the hierarchy structure. Combined with the assessment results of experts, a quantitative analysis and evaluation of the emergency response capacity of a coal enterprise was conducted by using FAHP. The comprehensive score of the enterprise's emergency response capability was 80.45, and the level of emergency response capacity was "good". The research results show that the D-FAHP method has high reliability in evaluating the emergency response capability of coal enterprises, avoiding the impact of uncertain and incomplete information on the assessment results. This can not only effectively identify the weak links in emergency management, but also meet the emergency decision-making needs of enterprises in the emergency state, which has important guiding significance to improve the ability and level of enterprise emergency management.

to statistics, China accounts for 70% of the world's coal mine casualties 7 . At present, the major accident disasters still occur frequently in Chinese coal mine, and the weak emergency ability is the main reason that leads to the serious consequences 8，9 . However, when the enterprise has a sound and perfect emergency management system, the loss caused by accidents will be reduced to 7% 10 . It can be seen that emergency capacity building play a vital role in coal enterprise, and the key to strengthen emergency capacity building is to carry out dynamic and continuous scientific assessment 11，12 .
In foreign countries, the earliest research on emergency management capability mainly focuses on the political field, and gradually extends to the evaluation of emergency management capability for typhoon, tsunami, hurricane, flash flood, waterlogging, fire and other emergencies 13,14 . In recent years, there are relatively few foreign studies on the emergency management capacity in the field of coal mine. However, the successful experience of emergency management in the disaster field has reference value for the study of the emergency capacity of coal mining enterprises.
In China, Miao Chenglin 15 proposed a theoretical model of the influence of habit field on the emergency response capability of coal mine emergencies, and verified the positive effect of this model on the emergency response capability with AMOS software. Sheng Yong 12,16 combed and constructed an enterprise emergency capability assessment system based on the bottom-line thinking and the method of scenario construction and deduction. Based on extension theory, some scholars studied the factors affecting emergency response ability from different perspectives and constructed an assessment system 17,18 . Some scholars 19,20 have integrated the open class method, entropy method and support vector machine to build an evaluation system of coal mine emergency capacity. Some scholars have constructed an indicator system of enterprise emergency response capability from the perspective of dynamic capability development and capability maturity, and adopted catastrophe progression to evaluate the emergency response capability 21,22 . In addition, there are structural equation model 23 , fuzzy comprehensive evaluation method 24 , analytic hierarchy process 25,26 and other evaluation methods.
Zhang 27 calculated the weight of each index of the evaluation model by using the analytic hierarchy process, and evaluated the miners' emergency capacity by using the fuzzy comprehensive evaluation method. Chen 28 proposed a coal mine emergency rescue ability evaluation model, which used intuitionistic fuzzy entropy method to calculate the index weight, and intuitionistic fuzzy weighted average operator to calculate the comprehensive evaluation matrix. According to the characteristics of diversity and uncertainty of information, Qi 29 proposed a multi-criteria comprehensive evaluation method based on interval binary representation model to avoid information distortion and loss in the process of linguistic information processing. Zhang 30 believed that the emergency assessment information was incomplete and uncertain, and proposed the method of using evidence theory to evaluate the city's emergency response capacity. Yang 31 analyzed the development and evolution process of coal mine emergency response capability by using Logistic curve, and evaluated the emergency response capability of coal mine enterprises based on fuzzy analytic hierarchy process.
In conclusion, in the assessment system of coal enterprises' emergency response capacity, some indicators are too qualitative, and some indicators are not operable or difficult to measure. The indicators are interrelated and influence each other. Meanwhile, the data processing is sketchy. As a result, the assessment results are lack of scientificity. Therefore, it is particularly significant to establish a scientific, measurable and operable index system for the assessment of coal enterprise emergency capacity.
It was difficult for experts to determine the degree of assessment when they used AHP, IAHP, FAHP and other methods to assess. These methods also did not consider the effect of incomplete information, which affected the reliability of the evaluation results. In addition, in order to make the evaluation results as independent as possible from personal preferences, the judgment matrix can be constructed through the expert group. But a feature vector that satisfies all judgment matrices is hard to find. In summary, these evaluation methods do not reflect people's perception of "uncertain" and "unknown" information. Based on this, the D number theory is integrated with AHP to avoid the non-consistent phenomenon of judgment matrix. This effectively solves the impact of information incompleteness and uncertainty on the evaluation results and avoids the mutual influence among the evaluation indicators of emergency capability. Furthermore, it can accurately assess the emergency response ability quantitatively, and provide theoretical support for improving the emergency response ability of coal mining enterprises.

D-S theory
Firstly, the identification framework of D-S theory is defined as the set of N mutually independent elements contained in the research target 32 , which is denoted by .  www.nature.com/scientificreports/ In practical application, D-S theory requires independent evaluation indexes and complete information, so this limitation makes it more suitable for dealing with uncertain problems with less data. Therefore, Deng 33,34 proposed an improved D-number theory on the basis of D-S theory.

D-number theory
Definition of D-number theory. (2) There exists D-number D and non-empty finite set C, then the information integrity Q of D can be quantified as follows.
(3) Let the discrete set �={b 1 , b 2 , . . . , b i , . . . , b n } , where, b i ∈ R , and when i = j , b i = b j , then the D number can be expressed as: or simply expressed as: where v i ≥ 0 and (4) ( Pe r m u t a t i o n i nv a r i a n c e ) , i f t w o D n u m b e r :

D-number preference relation.
The fuzzy preference relation reflects the relative importance of the evaluator to the decision-making scheme to a certain extent (represented by " ≻") 35 . Therefore, the fuzzy preference relation is adopted to construct the decision-making matrix.
Let there exist evaluation sample set A = {A 1 , A 2 , . . . , A n } , whose fuzzy preference relation is The meaning of matrix element r ij is the relative importance of A i and A j , which is expressed as: For example, if 10 experts are selected to evaluate the two schemes A1 and A2, the following results may occur: (1) Eight people thought A 1 ≻ A 2 with an importance of 0.7, and the other two people thought A 1 ≻ A 2 with an importance of 0.6.
(2) www.nature.com/scientificreports/ (2) Six people thought A 1 ≻ A 2 with an importance of 0.8, while the other four people did not evaluate the importance of A 1 and A 2 for prudent consideration or other reasons.
Due to the limitation of fuzzy preference relation, a reasonable matrix cannot be constructed when the information is uncertain. Therefore, D mathematical theory is adopted to improve the fuzzy preference relation, so that it can be applied in the field of uncertain and incomplete information. The improved evaluation matrix can be simply referred to as D-number preference matrix 36 .
Assume a set of assessment data A = {A 1 , A 2 , . . . , A n } , and its D-number preference relationship is: ij k represent the importance degree of plan i relative to plan j as considered by the evaluator k , and v ij k represents the support of the evaluator for the importance. Since the D-number preference relation can avoid the influence of the difference of evaluators' experience and ambiguity on their results, the above cases can be expressed as:

D-AHP method
The analytic hierarchy process (AHP) makes a multi-criteria decision by clarifying the influencing factors of the analysis object and forming a hierarchical structure, and comparing the relative importance of the elements of the hierarchical structure. Incompleteness of evaluation information limits the use of AHP method. Therefore, the D-AHP method is obtained by deeply integrating the D-number preference relationship with the AHP method. That is, AHP method is used to construct the hierarchical structure. The index weights of all levels are solved by the D-number preference relation to evaluate the decision-making problem in complex and uncertain environment. The hierarchy structure of D-AHP includes target layer, criterion layer and scheme layer. The weight solution process is as follows: Let the weight of criterion layer index C j j = 1, 2, . . . , m relative to target layer be w c j , w c j ≥ 0 and m j=1 w c j = 1 ; Let the weight of the evaluation object A j (i = 1, 2, . . . , n) of the scheme layer relative to the indicator C j of the criterion layer be w A i j , w A i j ≥ 0 and n i=1 w A i j = 1 . According to Eq. (9), the comprehensive weight of the evaluation object A i relative to the evaluation objective is solved:

Determination of weight of emergency capability evaluation index
Establishment of emergency capability evaluation system. The emergency response capability covers the whole process of pre-event prevention, incident response, in-process disposal and post-event management. Based on the research data of emergency management, an emergency response capability assessment system with 4 first-level indicators and 18 s-level indicators including prevention preparedness, monitoring and early warning, emergency response, accident handling and recovery is planned to be established. The hierarchy of each indicator is shown in Table 1.

Weight calculation based on D-AHP method.
(1) Use the fusion formula (1) to convert the D-number matrix R D into the real number matrix R C .
(2) The probability matrix R P is constructed according to matrix R C to represent the preference probability between two elements. Denote the elements of matrix R c as C ij , and denote the elements of matrix R p as: P ij = P r (C i ≻ C j ), ∀i, j ∈ {1, 2, ..., n}.
① When c ij + c ji = 1 , if c ij > 0.5 , then Pr(B i ≻ B j ) = 1;If c ij ≤ 0.5 , then pr(B i ≻ B j ) = 0. (3) Calculate the sum of each row in matrix R P , adjust the order of rows and columns in R P according to the size of each row sum, and obtain the triangulation matrix R T P . (4) According to the triangulation matrix R T P triangulation of the real matrix R C , the triangulated real matrix R T C is obtained. Where, when the elements of R T C meet: R T C (i, j) + R T C (j, i) < 1 , R T C needs to be further normalized to obtain the specification matrix R T C ′ , and the formula is as follows: The weight is calculated by introducing parameter , which is related to the cognitive ability of experts. The specific value formula of is as follows: where represents the lowest bound of , ⌈ ⌉ = min {K ∈ Z|K ≥ } . For example, if = 1.67 , then = ⌈ ⌉ = 2 . n represent the number of schemes.
Medium confidence in information n 2 2 , Low confidence in information www.nature.com/scientificreports/ Weight calculation. According to Table 1, the weight of each index in the emergency capacity index system is calculated.
(1) (1) Construct D matrix: (2) According to the fusion formula of D numbers, R D can be transformed into: (3) Construct probability matrix (4) Sort according to the sum size of each row in R p : Because in matrix R T C , R T C (2, 4) + R T C (4, 2) = 0.8 < 1 . Therefore, R T C is standardized: (6) Calculate the index weight according to R T C ′ Solution:    The assessment expert group is composed of emergency management researchers and managers with rich management experience. The assessment information is highly reliable, so = ⌈ ⌉ = 1 . The index weight of criterion layer is solved as w 1 = 0.455 , w 2 = 0.175 , w 3 = 0.275 , w 4 = 0.095 . That is, the weight of emergency prevention and preparation is 0.455, the weight of monitoring and early warning is 0.175, the weight of emergency treatment and rescue in the event is 0.275, and the weight of post-recovery is 0.095.
Similarly, the weight of each element of the indicator layer can be obtained, and the results are shown in Table 1. Due to space limitation, no detailed calculation will be made.

Result Analysis.
For the first-level indicators, the importance of the 4 indicators from high to low is emergency prevention and preparedness (C 1 ), emergency response and rescue (C 3 ), surveillance and early warning (C 2 ) and recovery and reconstruction (C 4 ).
For As emergency capacity building and upgrading requires as much human, material and advanced technical support as possible. Under the condition of being as objective as possible, the priority should be given to the construction of key elements according to the importance of quantified emergency capacity index, and then the construction of secondary elements should be supplemented and perfected. Then a dynamic, comprehensive, reasonable and efficient emergency system will be formed to meet the new needs of coal mine emergency management under the new situation.

Evaluation of emergency capacity of coal mining enterprises
Evaluation Process. According to the weight of each index determined by D-number theory and combined with Fuzzy Analytic Hierarchy Process (FAHP), the emergency capacity of a coal enterprise is evaluated.
(1) Establish the evaluation factor set The evaluation index system is constructed based on the factors that affect the emergency response capacity of coal mining enterprises, U = {U 1 , U 2 , . . . , U n } . For each subset, U i = {U i1 , U i2 , . . . , U in } . The factor set for emergency response capacity evaluation is composed of 4 first-level indicators in Table 1, and the sub-factors are composed of 18 s-level indicators.
(2) Establish the weight set Each factor has different degrees of influence on emergency response capability, and the degree of influence needs to be empowered for each factor. Determine the weight distribution of the factors at the next level to the factors at the previous level to form a weight set W = {W 1 , W 2 , . . . , W n } , n i=1 W i = 1 . According to the influence of each sub-factor to determine the weight of each sub-factor W i , 1]. W ij represents the weight of U ij in U i , and n represents the number of second-level indicators of U i . www.nature.com/scientificreports/ According to the evaluation results of experts, the index membership can be obtained, that is, the fuzzy relation matrix R = (r ij ) m×n can be generated. r ij represents the membership of the i factor to the j element.

(6) Calculate the comprehensive evaluation matrix
In this paper, the weighted average type fuzzy operator is used to calculate the evaluation vector B of emergency capacity. The calculation is carried out layer by layer from the lowest level to the first level of the evaluation index system, and the calculation is as follows: (7) Quantitative assessment of the emergency capacity of coal enterprises The 5 comments in the comment set are assigned, and the assignment matrix P is obtained, then P = (P i ) 5×1 .Then multiply the comprehensive evaluation matrix and the assignment matrix to obtain the quantitative evaluation value F of emergency response capability 37 .
In order to make a more intuitive quantitative analysis of the evaluation results, the scores of the 5 comments are graded as shown in Table 2, and P is assigned as: P1 = 90, P2 = 80, P3 = 70, P4 = 60, P5 = 50. Example analysis. The experts' scores on the subordination of the emergency response capacity of coal enterprises are shown in Table 3.
According to the membership degree and weight of each index, Eq. (14)  Therefore, the emergency capacity of the enterprise is Good.

Conclusion
(1) It is difficult to find a judgment matrix that meets the consistency when the evaluation is performed by AHP. It is difficult for experts to determine the membership degree of evaluation indicators, to evaluate uncertain information and incomplete information, and to avoid the interaction between evaluation indicators, which will affect the reliability of evaluation results. Therefore, the D-number theory is improved based on the D-S theory. Combining the theory of D-number with the analytic hierarchy process, the weights of 4 first-level indicators and 18 s-level indicators in the hierarchical structure model of emergency response capacity evaluation were calculated, and the weights and importance of each indicator were obtained. This effectively solves the evaluation under uncertain and unknown information, and avoids the interaction between evaluation indicators.  www.nature.com/scientificreports/ (2)According to the weight and importance calculation results of all levels of evaluation indicators, the importance of all level-1 and level-2 indicators was ranked respectively. Key indicators for emergency capacity building were identified. The fuzzy comprehensive evaluation method was used to construct the comprehensive evaluation matrix of emergency capability. Based on the results of evaluation experts and combined with the comprehensive evaluation and grading standard of emergency capability, the emergency capability of a coal enterprise was quantitatively evaluated. The final evaluation score was 80.45, and the evaluation result was "good", which was consistent with the actual situation of the enterprise's emergency response capacity. This provides a theoretical reference for the further construction and improvement of enterprise emergency capacity.
(3) According to the evaluation process of fuzzy analytic hierarchy process, the evaluation factor set, weight set and evaluation set of the secondary evaluation index are established. According to the expert evaluation results, the membership degree of the secondary index is determined, and then the comprehensive evaluation matrix is obtained. Combined with the importance of the secondary index and the assignment matrix, the paper makes a quantitative evaluation of the emergency capacity of coal enterprises. Finally, the overall evaluation score of the emergency capacity of a coal enterprise is 80.45 points, and the evaluation result is "good". The D-FAHP method can not only effectively identify the weak links in emergency management, but also meet the emergency decision-making needs of enterprises in an emergency state. It provides a new method for enterprise emergency capability assessment. www.nature.com/scientificreports/ Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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